Well, twelve years after I got a C- in 12th grade trig and rejoiced that I would never have to take math again, the gods have ordained that I take calculus. IT’S SO MUCH FUN, PEOPLE. Anyway, I’m crap at math and I’m stuck and my calc book was apparently written by syphilitic monkeys, so I turn to you, the Dopers, to help me.
How the hell can I convert the square root of x into a fraction? I want to say it would be 1/x^-1, but I could be wrong. In fact, I probably am.
HELP PLZ.
x^(1/2)
and in general the nth root would be x^(1/n)
And here’s how to see why that makes sense:
What does x^m mean? It means x * x … * x * x where there are m many xs in there (just as xm means x + x + … + x + x where there are m many xs in there); at least, it means this as long as m is a counting number so that this makes sense. But the nice properties generalize, since they’re what the general definition is based on.
So what can we say about x^(m + m)? Well, it’s what you get when you multiply a string of m + m many xs; but, of course, breaking that multiplication into parts by breaking that string into two halves, we see that this is just x^m * x^m.
So, x^(m+m) is the square of x^m. Thus, x = x^1 = x^(1/2 + 1/2) is the square of x^(1/2); that is to say, x^(1/2) is the square root of x. Does that make sense?
More generally, by the same kind of reasoning, we see that x^m * x^n = x^(m+n) and that (x^m)^n = x^(m*n), which are also good properties to know, and which explain why x^(1/n) should be an nth root of x.
I know the question has been answered, I just wanted to recommend SparkNotes Math Study Guides - SparkNotes if this is a general 1st year calculus course. I was in the exact same situation as you (about 10 years with no math after gleefully declaring that I would never crack a math book again), and these little ‘units’ helped me when I was lost.
THANK YOU!
Meyer6, thanks for the link - I bookmarked it. I was searching for something just like that the other day when I was completely baffled by my homework, and I strongly suspect it’ll happen again. I ended up watching some videos on YouTube. Turns out some math professors have made little animations about math and put them on the web. So helpful. How did we live without the internet, again?
Indistinguishable, аз разбрах твои пост точно колкото ти разбираш този пост. Разбираш ли?
P.S. Not that I don’t appreciate the effort.
No worries, although now I’m a little jealous that I didn’t think of the YouTube angle when I was going through my Calculus hell. Just as a word of support, I freaked right out about having to take that class, but I ended up getting an A+ in it - it turns out that you can get a long, long way by just turning up at every class and doing the homework, and it sounds like you’re on top of that. If your class is otherwise filled with party-hardy 18 year olds it also helps you to shine in comparison!
Да, аз разбирам.
FYI 1/x[sup]-1[/sup]=x or more specifically it equals x[sup]1[/sup].
I’ve been tutoring a few rugby buddies who have decided to go back to school. I’ve been able to tel them -how-, but I couldn’t articulate -why-. Thanks for that!
I don’t know how the original question was worded, but wouldn’t the square root of x expressed as a fraction be 1/(x[sup]-1/2[/sup])?
Of course, if you simply wanted to write the square root of x in exponential form, that would be x[sup]1/2[/sup].
:eek: I’m not the one to typically ask for medical advice in GQ, but dear dopers, seeing as how everybody else is seemingly not responding to this, I think I am actually hallucinating Bulgarians.
I think I caught your hallucination. I’m seeing not-English text as well.
So it’s all Greek to you, too?
It’s all Greek to me…
ouch, beaten by dr cube!